{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/jermwatt/machine_learning_refined/blob/main/notes/5_Linear_regression/5_3_Absolute.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J8VDN7C48-gw"
   },
   "source": [
    "## Chapter 5: Linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gVnaXM2G8-gx"
   },
   "source": [
    "# 5.3 Least Absolute Deviations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ha7I5BLL8-gy"
   },
   "source": [
    "In this Section we talk about a slight twist on the derivation of the Least Squares cost function that leads to an alternative cost for linear regression called *Least Absolute Deviations*.  This alternative cost function is much more robust to outliers in a dataset than the original Least Squares.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "sVoAkTZs8-gy",
    "outputId": "f418f673-48ad-4298-e929-18e40ee1524f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: github-clone in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (1.2.0)\n",
      "Requirement already satisfied: requests>=2.20.0 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (2.32.3)\n",
      "Requirement already satisfied: docopt>=0.6.2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (0.6.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.4.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.10)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2.2.3)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2024.12.14)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "chapter_5_datasets already cloned!\n",
      "chapter_5_library already cloned!\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "# install github clone - allows for easy cloning of subdirectories\n",
    "!pip install github-clone\n",
    "from pathlib import Path \n",
    "\n",
    "# clone datasets\n",
    "if not Path('chapter_5_datasets').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/5_Linear_regression/chapter_5_datasets\n",
    "else:\n",
    "    print('chapter_5_datasets already cloned!')\n",
    "\n",
    "# clone library subdirectory\n",
    "if not Path('chapter_5_library').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/5_Linear_regression/chapter_5_library\n",
    "else:\n",
    "    print('chapter_5_library already cloned!')\n",
    "\n",
    "# append path for local library, data, and image import\n",
    "import sys\n",
    "sys.path.append('./chapter_5_library')\n",
    "sys.path.append('./chapter_5_datasets') \n",
    "\n",
    "# import section helper\n",
    "import section_5_3_helpers\n",
    "\n",
    "# dataset paths\n",
    "data_path_1 = 'chapter_5_datasets/regression_outliers.csv'\n",
    "\n",
    "# standard imports\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# import autograd-wrapped numpy\n",
    "import autograd.numpy as np\n",
    "\n",
    "# this is needed to compensate for matplotlib notebook's tendancy to blow up images when plotted inline\n",
    "%matplotlib inline\n",
    "from matplotlib import rcParams\n",
    "rcParams['figure.autolayout'] = True\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iZjQ1TIZ8-gz"
   },
   "source": [
    "##  The susceptibility of the Least Squares cost to outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Io4hpuQQ8-gz"
   },
   "source": [
    "One downside of using the squared error in the Least Squares cost - as a measure that we then minimize to recover optimal linear regression parameters -  is that *squaring the error increases the importance of larger errors*.  In particular squaring errors of length greater than $1$ makes these values considerably larger.  This forces weights learned via the Least Squares cost to produce a linear fit that is especially focused on trying to minimize these large errors - often due to *outliers* in a dataset.   In other words, the Least Squares cost produces linear models that *tend to overfit to outliers in a dataset*.  \n",
    "\n",
    "We illustrate this fact via a simple dataset in the following example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j7f_wPPf8-g0"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 1: </span>  Least Squares overfits to outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bYta5dM18-g0"
   },
   "source": [
    "In this example we use the dataset plotted below - which can largely be represented by a proper linear model with the exception of a single large outlier - to show how the Least Squares cost function for linear regression tends to create linear models that *overfit* to outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "ZRouk_iq8-g0",
    "outputId": "4111b56a-223a-4bd0-f2a3-cf7ad3e16fb4"
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 900x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load in dataset\n",
    "data = np.loadtxt(data_path_1, delimiter = ',')\n",
    "x = data[:-1,:]\n",
    "y = data[-1:,:] \n",
    "\n",
    "# plot dataset\n",
    "demo = section_5_3_helpers.linear_regression_visualizer(data)\n",
    "demo.plot_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pmaPSkbR8-g1"
   },
   "source": [
    "We now tune the parameters of a linear regressor to this dataset by minimizing the Least squares cost via gradient descent.  $20$ steps are indeed sufficient in this case (as we can verify by visually examining the cost function history plot)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "1Vji5E__8-g1"
   },
   "outputs": [],
   "source": [
    "# compute linear combination of input point\n",
    "def model(x,w):\n",
    "    a = w[0] + np.dot(x.T,w[1:])\n",
    "    return a.T\n",
    "\n",
    "# an implementation of the least squares cost function for linear regression\n",
    "def least_squares(w):\n",
    "    cost = np.sum((model(x,w) - y)**2)\n",
    "    return cost/float(np.size(y))\n",
    "\n",
    "# run gradient descent to minimize the Least Squares cost for linear regression\n",
    "g = least_squares; w = np.array([1.0,1.0])[:,np.newaxis]; max_its = 100; alpha_choice = 10**(-1);\n",
    "weight_history_1,cost_history_1 = section_5_3_helpers.gradient_descent(g,alpha_choice,max_its,w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fm-kXv7F8-g2"
   },
   "source": [
    "Now we plot the linear model associated with those weights providing the smallest cost function value during the run below.  This fit (shown in black) does not fit the majority of the data points well, bending upward clearly to with the aim of minimizing the large squared error on the singleton outlier point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "yj2opHTA8-g2",
    "outputId": "9e292e62-476a-49fc-e534-cb69baf7383c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# grab best weights from minimization of Least Squares cost\n",
    "ind = np.argmin(cost_history_1)\n",
    "least_weights = weight_history_1[ind]\n",
    "demo.plot_fit(plotting_weights = [least_weights])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DSVH7sed8-g2"
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iuk38ANL8-g2"
   },
   "source": [
    "##  Replacing squared error with absolute error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Qb17CVPj8-g2"
   },
   "source": [
    "How can we make our linear regression framework more robust to outliers?  If we return the original derivation of the Least Squares cost function in the previous Section, our aim in learning a linear regressor is to learn a set of ideal weights so that \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathring{\\mathbf{x}}_{p}^T\\mathbf{w}^{\\,} \\approx \\overset{\\,}{y}_{p}^{\\,}  \\,\\,\\,\\,\\,\\,\\,\\, p=1,...,P\n",
    "\\end{equation}\n",
    "\n",
    "for a dataset of $P$ points $\\left \\{ \\mathbf{x}_p,\\,y_p \\right \\}_{p=1}^P$.  To learn these ideal weights the first step we took there was to square the difference between both sides of each desired approximation  - i.e., each error - above as \n",
    "\n",
    "\\begin{equation}\n",
    "g_p\\left(\\mathbf{w}\\right) = \\left(\\mathring{\\mathbf{x}}_{p}^{T}\\mathbf{w} - \\overset{\\,}{y}_p^{\\,}\\right)^2\n",
    "  \\,\\,\\,\\,\\,\\,\\,\\, p=1,...,P.\n",
    "\\end{equation}\n",
    "\n",
    "Each of these measures the *squared error* between model $\\mathring{\\mathbf{x}}_{p}^{T}\\mathbf{w}$ and $\\overset{\\,}{y}_p^{\\,}$.  Taking the average of these $P$ squared error terms gave us the Least Squares cost function.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9C_-1KKA8-g3"
   },
   "source": [
    " As an alternative to using a *squared* error for our point-wise cost we can instead measure the *absolute error* for each desired approximation\n",
    " \n",
    " \\begin{equation}\n",
    "g_p\\left(\\mathbf{w}\\right) =  \\left \\vert \\mathring{\\mathbf{x}}_{p}^{T}\\mathbf{w} - \\overset{\\,}{y}_p^{\\,}\n",
    "\\right \\vert  \\,\\,\\,\\,\\,\\,\\,\\, p=1,...,P.\n",
    "\\end{equation}\n",
    "\n",
    "By using absolute error instead of the squared variety we still treat negative and positive errors equally, but we do not exaggerate the importance of large errors greater than $1$ (since, of course, we do not square them).  If we form the average of these absolute error point-wise costs we have the cousin of Least Squares, the so-called *Least Absolute Deviations* cost function \n",
    "\n",
    "\\begin{equation}\n",
    "\\,g\\left(\\mathbf{w}\\right)=\\frac{1}{P}\\sum_{p=1}^{P} g_p\\left(\\mathbf{w}\\right) = \\frac{1}{P}\\sum_{p=1}^{P}\\left \\vert \\mathring{\\mathbf{x}}_{p}^{T}\\mathbf{w} - \\overset{\\,}{y}_p^{\\,}\n",
    "\\right \\vert.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9qko4uTt8-g3"
   },
   "source": [
    "The only price we pay in employing the absolute error instead of the squared error is a technical one: we are more limited in which optimization schemes we can apply to minimize the Least Absolute Deviations cost.  While this cost function is also always convex regardless of the input dataset, can only use zero / first order methods  to properly minimize it no second order methods (because the second derivative of this cost function is zero almost everywhere, as can easily be shown). \n",
    "\n",
    "Nonetheless, being limited to using local optimization methods like gradient descent is no severe condemnation - gradient descent is the most widely used optimization algorithm in machine learning / deep learning!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Vu9ebg_78-g3"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 2: </span>  Least absolute deviations versus Least Squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d_cwMQwT8-g3"
   },
   "source": [
    "With the sort of implementation philosophy described in the previous Section - where we break down a cost function into its basic components for modular implementation - we can think equivalently about the cost in equation (4) as\n",
    "\n",
    "\\begin{equation}\n",
    "\\,g\\left(\\mathbf{w}\\right)=\\frac{1}{P}\\sum_{p=1}^{P}\\left\\vert\\text{model}\\left( \\mathbf{x}_p,\\mathbf{w}\\right) -y_{p}^{\\,}\\right\\vert.\n",
    "\\end{equation}\n",
    "\n",
    "where we have denoted our linear `model` of the input and weights as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{model}\\left(\\mathbf{x}_p,\\mathbf{w}\\right) = \\mathring{\\mathbf{x}}_{p}^{T}\\mathbf{w}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KfYsBNwK8-g4"
   },
   "source": [
    "In implementing the cost in `Python` we can employ the ``model`` function we used with our Least Squares implementation shown in e.g., Example 1, since this is how we implement the linear combination of our input and weights.  All we then need to do is slightly alter the cost function itself to get our desired implementation, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "70v5wI4q8-g4"
   },
   "outputs": [],
   "source": [
    "# a compact least absolute deviations cost function\n",
    "def least_absolute_deviations(w):\n",
    "    cost = np.sum(np.abs(model(x,w) - y))\n",
    "    return cost/float(np.size(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "x84fzp4E8-g4"
   },
   "source": [
    "Below we plot the surface / contour plot of this cost function using the previously shown dataset - indeed it is convex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 369
    },
    "id": "vCrZTx1T8-g4",
    "outputId": "7cccd229-9b9f-4f4d-a1f2-b8c2b36337d2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# show run in both three-dimensions and just the input space via the contour plot\n",
    "section_5_3_helpers.static_visualizer().two_input_surface_contour_plot(least_absolute_deviations,[],view = [10,70],xmin = -4.5, xmax = 4.5, ymin = -4.5, ymax = 4.5,num_contours = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2-gjvX0X8-g4"
   },
   "source": [
    "Below we run gradient descent for $100$ iterations, using the same choice of steplength parameter as used in the previous example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "g9SDsjrS8-g4"
   },
   "outputs": [],
   "source": [
    "# run gradient descent to minimize the Least Squares cost for linear regression\n",
    "g = least_absolute_deviations; w = np.array([1.0,1.0])[:,np.newaxis]; max_its = 100; alpha_choice = 10**(-1);\n",
    "weight_history_2,cost_history_2 = section_5_3_helpers.gradient_descent(g,alpha_choice,max_its,w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4B7-1ilt8-g5"
   },
   "source": [
    "Now we plot and compare the best fit found via gradient descent for both cost functions on the dataset.  The Least Squares fit is shown in black, while the Least Absolute Deviation fit is shown in magenta.  The latter fits considerably better, since it does not exaggerate the large error produced by the single outlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "7OegS_qm8-g5",
    "outputId": "d160e957-ed8c-4c10-9911-b83b2ee7f038"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JVSc1LoY81aetQgifA4uBZ4FhMcaPV3Ls3sDEFdoeAQ5f2YuHEFoCLSs1tVv7UiVJUn1YsGAB1157LRdffDFfffVVVt9hhx1Gfn4+P/rRjxKqTmqcDHmqL88DA4DpQDfgIuC/IYQdY4zzqzm+K/DlCm1flrevzLDy15UkSQ1ccXExV111FRMnTuSbb77J6jvqqKPIy8ujd+/eyRQnNXKGPNWLGOM/Kz19PYTwPPARcDRwcy29zRiyr/61Az5dybGSJCkB3333HVdccQWXXnop3333XUV7CIGjjz6avLw8dtxxx+QKlFLAkKdExBi/CyG8B/RaySFfABut0LZRefvKXrMEKFn+3JW2JElqOL755hsuu+wyrrjiCoqLiyvac3JyOPbYYxk+fDjbbbddghVK6WHIUyJCCOsBPYE7VnLIs8D+wGWV2g4sb5ckSY3EnDlzuOSSS7j66qtZsGBBRXtubi5//OMfGT58OFtttVWCFUrpY8hTvQghXAw8SGaK5sbA/wNKyWyTQAjhduCzGOOw8iGXA0+GEC4AHgL6AT8CTq7n0iVJ0lr44osvuPjii7n22mv5/vvvK9qbN2/OgAEDGDp0KD169EiwQim9DHmqL5uSCXTrA3OAp4G9Yoxzyvu7A2XLD44xPhNCOBYYCYwG3gcOd488SZIats8++4zx48dzww03sHjx4or2Fi1acOKJJzJkyBC6d++eYIVS+oUYY9I1SHUihNAemDdv3jzat2+fdDmSJKXaxx9/zLhx47jppptYsmRJRXurVq04+eSTufDCC9lkk00SrDBbcXExHTp0AOgQYyxe3fFSY+KVPEmSJK21Dz74gDFjxjBp0iSWLl1a0d6mTRtOO+00Bg0aRNeuq9oBSVJtM+RJkiRpjc2YMYPRo0dz++23U1paWtHetm1bzjzzTM4//3w23HDDBCuUmi5DniRJkmrs3XffZdSoUfz5z3+mrKzidnrat2/P2Wefzbnnnsv666+fYIWSDHmSJElarTfffJNRo0YxZcoUKq/p0LFjR8477zzOPvtsOnbsmFyBkioY8iRJkrRSr776KiNHjuTee+/Nau/cuTMXXHABZ555pgucSQ2MIU+SJElVvPTSSxQVFfG3v/0tq71Lly4MGjSI0047jXbt2iVUnaRVMeRJkiSpwnPPPUdRURH/+Mc/stq7du3KhRdeyMknn0zbtm0Tqk5STRjyVCGE8A9g+xjjFiu0B+BlYGGM8WdJ1CZJkurW008/TWFhIf/617+y2jfZZBOGDh3KCSecQOvWrROqTtKaMOSpsheBg0MInWKM31Zq7wfsCvw0mbIkSVJdiDHy5JNPUlhYyBNPPJHV1717d4YNG8bAgQNp2bJlQhVKWhuGPFX2UvnXXYHHAUIIzYEi4MEY4/+SKkySJNWeGCP//ve/KSws5Omnn87q69GjB8OHD+ePf/wjLVq0SKhCSevCkKfKXiz/uhvlIQ84GdgSODyJgiRJUu2JMfLPf/6ToqIinnvuuay+rbbairy8PI499liaNfNbRKkx80+wKsQYvwghfEbmSh4hhLZAPjA5xvhmosVJkqS1FmPkwQcfpLCwkJdffjmrb7vttiMvL49jjjmG3NzchCqUVJsMeVrRi5SHPOB8oBNQkFw5kiRpbZWVlfHXv/6VoqIiXnvttay+HXfckfz8fI466ijDnZQyhjyt6EXgsBBCd2AQcG2M8aOEa5IkSWugtLSUqVOnUlRUxFtvvZXV17t3bwoKCvjd735HTk5OQhVKqkuGPK3oJSAH+DMQgFHJliNJkmpq2bJl3H333YwaNYp33303q+/HP/4xBQUFHHLIIWR2R5KUVoY8rWj5Cpv7AP8XY5yTZDGSJGn1li5dyp133smoUaOYMWNGVt/ee+9NQUEBv/71rw13UhNhyFOWGOPcEMKHQFvgkoTLkSRJq7BkyRJuu+02Ro8ezYcffpjV9/Of/5yCggJ++ctfGu6kJsaQpywhhB7AZsD5McYFSdcjSZKqWrx4Mbfccgtjx47lk08+yerbf//9yc/PZ999902oOklJM+RpRWOAD4HrEq5DkiStYNGiRdx4442MGzeOzz//PKvv17/+Nfn5+eyzzz4JVSepoTDkiRBCR+BgYD+gL3BwjHFJkjVJkqQfLFy4kOuuu44JEybw5ZdfZvX99re/JT8/nz322COh6iQ1NIY8AexPZjXNT4FTYoyPJFyPJEkC5s+fzzXXXMPFF1/M119/ndV3+OGHk5+fz2677ZZQdZIaKkOeiDHeS2a7BEmS1ADMmzePK6+8kksvvZS5c+dWtIcQ6NOnD3l5eey8884JViipITPkSZIkNRDffvstl19+OZdddhnz5s2raM/JyeGYY45hxIgR7LDDDglWKKkxMORJkiQl7Ouvv+bSSy/lyiuvZP78+RXtubm59O/fn+HDh7PNNtskWKGkxsSQJ0mSlJAvv/ySSy65hGuuuYaFCxdWtDdr1ozjjz+eYcOG0bNnzwQrlNQYGfIkSZLq2ezZs5kwYQLXXXcdixYtqmhv3rw5f/rTnxg6dChbbLFFcgVKatQMeZIkSfXk008/Zdy4cdx4442UlJRUtLds2ZKTTjqJCy+8kM022yzBCiWlgSFPkiSpjn300UeMHTuWW265hSVLftiKtnXr1pxyyikMHjyYjTfeOMEKJaWJIU+SJKmOzJw5kzFjxnDbbbexbNmyivY2bdpwxhlncMEFF7DRRhslWKGkNDLkSZIk1bL33nuP0aNHM3nyZEpLSyva11tvPc466yzOO+88unTpkmCFktLMkCdJklRL3n77bUaNGsXdd99NWVlZRXuHDh0455xzOOecc+jcuXOCFUpqCgx5kiRJ6+iNN95g5MiR3HPPPcQYK9o7derE+eefz5lnnknHjh2TK1BSk2LIkyRJWkvTpk2jqKiIv/71r1ntG2ywARdccAGnn3467du3T6g6SU2VIU+SJGkNvfjiixQVFfHggw9mtW+00UYMHjyYU089lbZt2yZUnaSmzpAnSZJUQ8888wxFRUU8/PDDWe0bb7wxF154ISeddBJt2rRJqDpJyjDkSZIkrcZTTz1FYWEhjz32WFb7pptuyrBhw/jTn/5Eq1atEqpOkrIZ8iRJkqoRY+SJJ56gsLCQJ598Mqtv8803Z/jw4Rx//PG0bNkyoQolqXqGPEmSpEpijDz66KMUFhbyzDPPZPX17NmTESNG8Ic//IHmzZsnVKEkrZohT5IkiUy4e+ihhygqKuKFF17I6ttmm23Iy8ujX79+NGvmt0+SGjb/lpIkSU1aWVkZf/vb3ygsLGTatGlZfdtvvz35+fn07duX3NzchCqUpDVjyJMkSU1SWVkZ9957LyNHjuT111/P6tt5553Jz8/nyCOPJCcnJ6EKJWntGPIkSVKTUlpayl/+8hdGjhzJ22+/ndW32267UVBQwKGHHmq4k9RoGfIkSVKTsGzZMv785z8zatQo3nvvvay+Pffck4KCAg4++GBCCAlVKEm1w5AnSZJSbenSpdxxxx2MGjWKWbNmZfXts88+FBQUcOCBBxruJKWGIU+SJKVSSUkJkyZNYsyYMXz00UdZffvttx8FBQXst99+hjtJqeNkc9WLEMKwEMKLIYT5IYSvQgj3hxC2Wc2YASGEuMJjcX3VLElqnBYvXsxVV11Fr169OPXUU7MC3oEHHshTTz3FE088wS9+8QsDnqRU8kqe6su+wNXAi2R+340GHg0hbB9jXLiKccVA5TAY665ESVJj9v3333PDDTcwfvx4Zs+endV38MEHk5+fz957751QdZJUfwx5qhcxxoMqPw8hDAC+AnYHnlr10PhFHZYmSWrkFixYwLXXXsvFF1/MV199ldV32GGHkZeXx49//OOEqpOk+mfIU1I6lH+du5rj1gshfERmavErwPAY41vVHRhCaAm0rNTUbp2rlCQ1WMXFxVx99dVccsklfPPNN1l9Rx55JHl5eey6664JVSdJyTHkqd6FEHKAy4D/xRjfXMWh04E/Aa+TCYWDgGdCCDvEGD+t5vhhwEW1XK4kqYH57rvvuOKKK7jsssv49ttvK9pDCBx99NGMGDGCnXbaKcEKJSlZIUZvcVL9CiFcCxwM/HQlYW1l45oD7wB3xRjzq+mv7krep/PmzaN9+/brWLUkKWlz587lsssu4/LLL6e4uLiiPScnh9///veMGDGC7bbbLsEK1ZgUFxfToUMHgA4xxuLVHS81Jl7JU70KIVwF/Bb4+ZoEPIAY49IQwjSg10r6S4CSSu+1LqVKkhqIOXPmMHHiRK666ioWLFhQ0Z6bm8sf//hHhg8fzlZbbZVghZLUsBjyVC9CJnFdCRwB7Bdj/GAtXiMX2An4Ry2XJ0lqgL744gsuvvhirr32Wr7//vuK9mbNmjFw4ECGDh1Kjx49EqxQkhomQ57qy9XAscDvgPkhhK7l7fNijIsAQgi3A5/FGIeVPy8AngNmAB2BwcDmwE31W7okqT59/vnnjB8/nuuvv57Fi3/YHrVFixaccMIJDBkyhM033zzBCiWpYTPkqb6cVv71Pyu0DwQmlf+6O1BWqa8TcCPQFfgWeBn4SYzx7TqrUpKUmI8//phx48Zx8803U1JSMfueVq1acfLJJzN48GA23XTTBCuUpMbBhVeUWiGE9sA8F16RpIbtgw8+YOzYsdx6660sXbq0or1169acdtppDBo0iG7duiVYodLIhVeUZl7JkyRJiZgxYwajR4/m9ttvp7S0tKK9bdu2nHnmmZx//vlsuOGGCVYoSY2TIU+SJNWr6dOnM2rUKO68807Kyn6Ypd++fXvOOusszj33XDbYYIMEK5Skxs2QJ0mS6sVbb73FyJEjmTJlCpVvF+nYsSPnnnsuZ599Np06dUqwQklKB0OeJEmqU6+99hpFRUXce++9We2dO3fmggsu4Iwzzlh+b5QkqRYY8iRJUp14+eWXKSoq4oEHHshq79KlC4MGDeK0006jXbt2CVUnSellyJMkSbXq+eefp6ioiIceeiirvWvXrlx44YWcfPLJtG3bNqHqJCn9DHmSJKlWPP300xQVFfHoo49mtW+yySYMGTKEE088kdatWydUnSQ1HYY8SZK01mKMPPnkkxQWFvLEE09k9XXv3p1hw4YxcOBAWrZsmVCFktT0GPIkSdIaizHy2GOPUVhYyH//+9+svi233JLhw4dz3HHH0aJFi4QqlKSmy5AnSZJqLMbIww8/TGFhIc8991xW31ZbbcWIESM49thjad68eUIVSpIMeZIkabVijDz44IMUFRXx0ksvZfVtu+225OXlccwxx9Csmd9aSFLS/JtYkiStVFlZGffffz9FRUW8+uqrWX077rgj+fn5HHXUUeTm5iZToCSpCkOeJEmqorS0lKlTpzJy5EjefPPNrL7evXtTUFDA7373O3JychKqUJK0MoY8SZJUYdmyZdx9992MGjWKd999N6vvRz/6EQUFBfz2t78lhJBQhZKk1THkSZIkli5dyp133smoUaOYMWNGVt9ee+3FRRddxK9//WvDnSQ1AoY8SZKasCVLlnD77bczevRoPvjgg6y+n/3sZxQUFLD//vsb7iSpETHkSZLUBJWUlHDLLbcwduxYPv7446y+X/7ylxQUFLDvvvsmVJ0kaV0Y8iRJakIWLVrEjTfeyPjx4/nss8+y+n7961+Tn5/PPvvsk1B1kqTaYMiTJKkJWLhwIddffz3jx4/nyy+/zOo75JBDyM/PZ88990yoOklSbTLkSZKUYvPnz+eaa67hkksuYc6cOVl9hx9+OHl5eey+++4JVSdJqguGPEmSUmjevHlcddVVTJw4kblz51a0hxA46qijyMvLY5dddkmwQklSXTHkSZKUIt9++y2XX345l19+Od99911FewiBfv36MWLECHbYYYfkCpQk1TlDniRJKfDNN99w6aWXcsUVVzB//vyK9tzcXPr378/w4cPZZpttEqxQklRfDHmSJDViX331FZdccglXX301CxcurGhv1qwZxx13HMOGDaNXr14JVig1QN9B7jO5SVch1RlDniRJjdDs2bOZMGEC1113HYsWLapob968OX/6058YOnQoW2yxRXIFSg1BBGYD01Z4fABtaZtkZVKdMuRJktSIfPrpp4wfP54bbriBkpKSivaWLVty4oknMmTIEDbbbLMEK5QSUgbMpGqg+yrJoqRkGPIkSWoEPvroI8aOHcstt9zCkiVLKtpbtWrFqaeeyuDBg9l4440TrFCqR0uAt8kOc68B81c1qFwbYBdYssMSuKnuSpSSZMiTJKkBmzVrFmPGjGHSpEksW7asor1NmzacfvrpXHDBBXTt2jXBCqU6toBMgKsc6N4iE/RWZ31g1xUeWwG5sLh4sSFPqWXIkySpAXrvvfcYPXo0kydPprS0tKJ9vfXW46yzzuK8886jS5cuCVYo1YE5VJ1u+T6Ze+tWpztVA92mQKiTSqUGzZAnSVID8s477zBq1CjuuusuysrKKto7dOjAOeecwznnnEPnzp0TrFCqBRH4iKqB7rMajM0BtiE7zPUmc9VOEmDIkySpQXjjjTcYOXIk99xzDzH+cNmiU6dOnHfeeZx11ll07NgxuQKltbUMmE52mHsV+LYGY1sCO5Ed6HYCF8aUVs2QJ0lSgqZNm0ZRURF//etfs9rXX399Bg0axOmnn0779u0Tqk5aQ4uAN8gOdK8Di2swtgOZK3KVA922QPO6KFRKN0OeJEkJePHFFykqKuLBBx/Mat9www0ZPHgwp556Kuutt15C1Uk18C2ZK3KVA927QOkqxizXjar3z22J989JtcSQJ0lSPXr22WcpLCzk4Ycfzmrv1q0bQ4YM4aSTTqJNmzYJVSdVIwKfU/X+uQ9rOL4XVQPdRrVepaRKDHmSJNWDp556iqKiIv79739ntW+66aYMHTqUE044gVatWiVUnVSuDJhB1UA3pwZjmwE7kB3mdgGcbSzVO0OeJEl1JMbIE088QWFhIU8++WRW3+abb87w4cM5/vjjadmyZUIVqklbQma/uRU3FF9Qg7FtyQS4yoFuBzILpUhKnCFPkqRaFmPk0UcfpaioiP/9739ZfT179mTEiBH84Q9/oHlzV5RQPZlP9RuKL63B2A2oOt2yF5BbJ5VKqgWGPEmSakmMkX/84x8UFhbywgsvZPVtvfXW5OXl8fvf/55mzfznV3XoK6pOt5xBzTYU35yqgW4TXBBFamT8V0aSpHVUVlbG3/72N4qKinjllVey+rbffnvy8vI4+uijyc310odqUQQ+oOoKl5/XYGwOme0JVtxQvHMd1Cmp3hnyJElaS2VlZdx3330UFRXx+uuvZ/XtvPPO5Ofnc+SRR5KTk5NQhUqNZcA7VN1QfF4Nxrai+g3FXcRVSi1DniRJa6i0tJS//OUvjBw5krfffjurb7fddqOgoIBDDz3UcKe18z3E1yLxlUjJ8yWUvlRK21ltCSU1mDPZkeo3FPc7PqlJ8Y+8JEk1tGzZMu666y5GjhzJe++9l9W3xx57UFBQwG9+8xtC8AYm1dBcqtw/F6dHQlkgEGhN65WP3YSq0y23wPvnJBnyJElanaVLl3LHHXcwevRoZs6cmdW3zz77UFBQwIEHHmi408pF4FOqLojycdVDwwoprYwy3ud9pjGNsl3KOGbMMeTungsb1nnVkhopQ54kSStRUlLCpEmTGDt2LB9++GFW33777UdBQQH77bef4U7ZSoH3qXr/3Nc1GNsclm67lDvevINX4itMYxqv8zoLyjevy30zlwN/dCBdunSpo+IlpYEhT/UqhHAGMBjoSmbHnrNijC+s4vi+QBGZCSjvA0NijP+oh1IlNWGLFy/m5ptvZuzYsXz66adZfQcccAD5+fn8/Oc/T6g6NSglwJtkB7rXgYU1GLseVe+f2x5efuVlTtj7hGqHlJaWMmvWLEOepFUy5KnehBCOASYCpwLPA+cCj4QQtokxflXN8T8B7gKGAX8HjgXuDyHsFmN8s94Kl9RkfP/999xwww2MHz+e2bNnZ/UdfPDB5Ofns/feeydUnRJXTNXtCt4ms/Ll6mxI1f3nepLZymAFPXv2JDc3l9LS0ip9ubm59OjRY63Kl9R0hBhrsjOmtO5CCM8DL8YYzyx/ngN8AlwZYxxbzfFTgLYxxt9WansOeDXGeGoN3q89MG/evHm0b9++tk5DUgotWLCA6667jgkTJvDVV9k/czrssMPIy8vjxz/+cULVKRFfUPX+uZmrHPGDLaka6LpR4wVRSktL6d+/P1OmTKnS169fPyZPnuyei7WguLiYDh06AHSIMRYnXY9Um7ySp3oRQmgB7A6MWd4WYywLIfwbWNmPxfcmc+WvskeAw+uiRklNT3FxMVdffTUTJ07k66+zb5g68sgjycvLY9ddd02oOtWLCMyiaqD7ogZjc4HtqLrCZcd1KyknJ4dJkyYRQuCee+6htLSU3Nxc+vbty6233urWHJJWy5Cn+rIBmX8Ov1yh/UsyO/hUp+tKju9a3cEhhJZAy0pN7da8TElNwXfffceVV17JpZdeyrffflvRHkKgb9++5OXlsdNOOyVYoerEUqrfULwm13BaAzuTHeh2LG+vZSEEWrZsyeTJk7niiiuYNWsWPXr0oHPnzuTk5LjQj6TVMuQpTYYBFyVdhKSGa+7cuVx22WVcfvnlFBf/8J19Tk4Ov//97xkxYgTbbbddghWq1iwkswBK5UD3JpmFUlanE1WnW25NvX7XFEIgNzeXLl26uMiKpDVmyFN9+ZrMotIbrdC+ESufFPPFGh4/huzpne3I7EokqYmbM2cOEydO5KqrrmLBggUV7bm5ufzxj39k+PDhbLXVVglWqHXyDVWnW04nMxVzdTalaqDrjhuKS2rUDHmqFzHGJSGEl4H9gfuhYuGV/YGrVjLs2fL+yyq1HVjeXt17lFDpZ7ROZ5H05ZdfcvHFF3PNNdfw/fffV7Q3a9aMAQMGMGzYMFcqbEwimeW6Vgx0n9RgbCBzNW7FQLdBnVQqSYky5Kk+TQRuCyG8BLxAZguFtsCtACGE24HPYozDyo+/HHgyhHAB8BDQD/gRcHI91y2pkfn8888ZP348119/PYsXL65ob9GiBSeccAJDhgxh8803T7BCrVYp8B5VA93cGoxtQeZ+ucphbmcy+9JJUhNgyFO9iTFOCSF0AQrJLJ7yKnBQjHH54irdgbJKxz8TQjgWGAmMJrMZ+uHukSdpZT755BPGjRvHTTfdREnJDzdftWrVipNOOokLL7yQTTfdNMEKVa3FVL+h+PerGlSuHVU3FN+OTNCTpCbKffKUWu6TJzUdH374IWPGjOHWW29l6dKlFe2tW7fmtNNOY9CgQXTr1i3BClVhHtVvKF513++qNqLqdMseVLuhuLQ67pOnNPNKniSp0ZoxYwZjxozh9ttvZ9myZRXtbdu25YwzzuCCCy5gww03TLDCJm42Vadbzqrh2B5Uv6G4JGm1DHmSpEZn+vTpjBo1ijvvvJOysopZ3rRr146zzz6bc889lw02cEWNelMGzKTq/nMr7nRanWbA9mRPuewNdKj9MiWpqTDkSZIajbfeeotRo0Zx9913U/l2g44dO3Luuedy9tln06lTpwQrbAKWkJleWTnQvQbMr8HYNmRvKL4bsAPQqk4qlaQmy5AnSWrwXnvtNUaOHMnUqVOz2jt37sz555/PmWeeufzeGtWmBWQCXOVA9xaZoLc66/PDVbnKG4rn1kWhkqTKDHmSpAbr5ZdfpqioiAceeCCrvUuXLgwaNIjTTjuNdu3aJVRdysyh6v1z71OzDcW7Q9w1EneJzO81n5ntZ7LZ3pvRef3O5OTkuG+pJNUzQ54kqcF5/vnnKSoq4qGHHspq79q1K4MHD+aUU06hbdu2CVXXyEXgI6oGus9qMDYH2IbsxVB6Q+wcKSkpYcCAAUwdNZXS0lJyc3Pp06cPkyZNomXLlgY9SapHhjxJUoPxv//9j8LCQh599NGs9o033pihQ4dy4okn0rp164Sqa4SWAdOpuiDKtzUY2xLYiexAtxNQTbYuKy1jwIABTJkypaKttLSUKVOmEEJg8uTJ5OY6T1OS6ov75Cm13CdPajyefPJJCgsLefzxx7Pau3fvztChQxk4cCCtWrk6xyotAt6g6obii2swtgNVNxTfFmhes7eeM2cO3bp1o7S06mZ3ubm5zJ49my5dutTsxaR64j55SjOv5EmSEhFj5LHHHqOwsJD//ve/WX1bbrklw4cP57jjjqNFixYJVdiAfUvVDcXfpWYbinej6v5zWwLrMJty5syZ1QY8yFzRmzVrliFPkuqRIU+SVK9ijDz88MMUFRXx7LPPZvX16tWLvLw8jj32WJo3r+FlpDSLwOdUvX/uwxqO70XVQLdRrVdJz549yc3NXemVvB49etT+m0qSVsqQJ0mqFzFG/v73v1NYWMhLL72U1bftttuSl5fHMcccQ7NmTfSfpjJgBlUD3ZwajG1GZr+5ymFuF6CeZqp37tyZPn36ZN2Tt1zfvn3p3Llz/RQiSQIMeZKkOlZWVsb9999PUVERr776albfjjvuSF5eHn369GlaC3MsIbPf3Iobii+owdi2ZAJc5UC3A5mFUhKSk5PDpEmTCCFwzz33VKyu2bdvX2699VZycnKSK06SmiAXXlFqufCKlKzS0lKmTp3KyJEjefPNN7P6evfuTX5+Pocffnj6A8B8qt9QfGkNxm5A1emWvWiQG4rHGCkrK2Pu3LnMmjWLHj160Lmz++Sp4XLhFaWZV/IkSbVq2bJlTJkyhZEjR/Luu+9m9f3oRz+ioKCA3/72t+n8xv8rqk63nEHNNhTfnKqBbhPWaUGU+hRCIDc3ly5durjIiiQlzJAnSaoVS5cu5c9//jOjRo3i/fffz+rba6+9KCgo4KCDDkpHuItkFj9ZMdB9XoOxOWS2J1hhQ3G8bU2SVEsMeZKkdbJkyRJuv/12Ro8ezQcffJDV97Of/YyCggL233//xhvulpHZnmDFDcW/q8HYVlS/oXibOqhTkqRyhjxJ0lopKSnhlltuYezYsXz88cdZfb/85S8pKChg3333rdX3jDESY2Tu3LnMmDGDnj171u59X9+T2UD8VX4IdG9Qsw3FO1L9huL+SytJqmf+0yNJWiOLFi3ipptuYty4cXz22WdZfb/61a/Iz8/npz/9aa29X+UFPWbMmMEWW2xBp06dePTRRykqKuKoo45i0qRJtGzZcs2C3lyqTrecTmYrg9XZmKr3z21Bo7l/TpKUboY8SVKNLFy4kOuvv54JEybwxRdfZPUdcsgh5Ofns+eee9bqe8YYKSkpYcCAAUydOrViaf4+ffpw0003AXDRRRcRQmDy5MnVb8MQgU+pGug+rnpotbaiaqDbcB1PTJKkOuQWCkott1CQasf8+fO59tprufjii5kzJ3tn7t/97nfk5+ez++6718l7l5aW0r9//2o32e7Xrx+33norm2yyCfPmzWP27Nl06dwF3qfq/XNf1+DNmgM7kh3mdgba1c65SGpY3EJBaeaVPElStebNm8dVV13FxIkTmTt3blZfnz59yMvLY5dddqnTGubOncvUqVOr7XvgLw9QfFwxl+90OfOenEer/VvBLGBhDV54PareP7c90KJ26pYkKUmGPElSlm+//ZYrrriCyy67jO+++66iPYRAv379GDFiBDvssEO91DJz5kxKS0tpRzt605tdK/23fdn2NP9Nc/7AHzIHv7GSF9mQqtMte5LZykCSpBQy5EmSAPjmm2+49NJLufLKKyku/mHmUk5ODv3792f48OFsu+22dV/IF1RMtdz1uV15n/fpRa+ajd2SqoGuGy6IIklqUgx5ktTEffXVV1xyySVcffXVLFz4w1zHZs2acdxxxzFs2DB69aphyFoTkcz0yhUXRKm0pktLWlYb8JaxjM87fM4mh2zC1JlTOaLwCJr/uDmhk2lOkiRDniQ1UbNnz+biiy/m2muvZdGiRRXtzZs3Z+DAgQwdOpQtt9yydt5sKfAOVRdEqcFSB7F1ZEabGTw29zFeia/wes7rbH3k1lx/+/UsKl1En9Z9am+fPEmSUsCQJ0lNzKeffsr48eO58cYbWbz4h12+W7RowUknncSFF15I9+7d1/4NFpLZULxyoHsTKKnB2E5UnW65FfTI6UHHuR3Zddau9OjRo3Y3QJckKWUMeZLURHz00UeMGzeOm2++mSVLllS0t2rVilNOOYXBgwezySabrNmLfkPV6ZbvUbMNxTelaqDrTpX75wKBXHLp0qULXbp0WbP6JElqggx5kpRys2bNYsyYMUyaNIlly5ZVtLdp04ZTTz2VgQMHsmDBAlq0aEFpaWn1V8gi8AlVA90nNSggAFuTHeZ6A+Y1SZLqhCFPklIgxkhZWRlz585l5syZ9OzZk2+++YZx48Zxxx13UFpaWnHseuutxxlnnMEZZ5zB4MGD6d27N6WlpeTm5tKnTx8m3TyJlh+1JLwasgPd3JW9eyUtqH5D8fVq/ZQlSdJKGPIkqZGLMVJSUsKAAQOYOnUqpaWlFVfiYowVx7Vv355zzjmHc889lw4dOtC/f3/un3L/D/vPle7KrlN2hakQSmtwr1s7qm4ovh1uKC5JUsJC5W8ApDQJIbQH5s2bN4/27dsnXY5UZ0pLS+nfvz9Tpkyptr9Tp06cd955nHXcWXT8sCNMg8XPLua9v7zH9mxPs5r8vG8jqt4/1wM3FJfUaBUXF9OhQweADjHGGqz1KzUehjylliFPTcXjjz/O/vvvn9XWla7syq7sxm4MPWgo6723XmZPuhqYyUw6/aITnffvnL2hONVPC3WlS0mNkSFPaeZ0TUlqpF566SVGFo7kzQffpA99MlMuy//rStcfDny4+vHLWMbbvM20Sv+9yqsszF3I7CmzqyyMUt200Ir7+CZNomXLlgY9SZIaAEOeJDUWS4B3YMY9M3hr8lt0+qgTt3M77anBleo2ZBZAKb8yV7pzKQMvHsjkqZOrHNqvbz86d+5cpb2srIwBAwZkTQstLS1lypQphBCYPHkyubm5a316kiSpdjhdU6nldE01aguA18ha3bLszTJylq7+Jrhv+KbiylyrvVpx+o2nk7tdLlTKX8uvyg0cOJB77rmn4qpc3759ufXWW6u9Kjdnzhy6deuWtVLncrm5ucyePdt97CQ1Gk7XVJp5JU+SkjaHqvvPvU9mb7pKcqpZ5WR+p/m02acNcZfIZU9extXPXM2HZR9mBbacljlVNxgPgZYtWzJ58mSuuOIKZs2aRY8ePVZ5f93MmTOrDXiQuaI3a9YsQ54kSQ2AV/KUWl7JU4MTgY+oGug+W/3QUkqZznSmMY1POn9C74G92X/Q/jTv2jzz0pUWRKlJYFsbXsmTlCZeyVOaeSVPkurCMmA62WHuVeDb1Q8tbV7K9BbTeXrh0xXTLt/gDTbdelPy8vIY9PtBNGuW/dd3CIHc3Fy6dOlSZ0Grc+fO9OnTp9qtGvr27VvtfXySJKn+GfIkaV0tAt4gO9C9Ud6+Oh2A3hB7R6YxjXGPjuO+d+5j2dJlFYdsv/323JR3E0cffXSiC5vk5OQwadIkQgjV3seXk+OmeZIkNQRO11RqOV1TdeJbMlfkKge6d4Hqb1XL1o0qG4qXbV7GfX+9j5EjR/Laa69lHb7zzjuTn5/PkUce2WACVH1MC5Wk+uB0TaWZV/IkqToR+JyKIBenRZgG4cMaBpleVAl0bPRDd2lpKX/5y18Yddgo3nrrrayhu+22G/n5+Rx22GENJtwtVx/TQiVJ0rox5ElSGTCDqguizPnhkLDi8pTlYrMIO0DYNfwQ5naBlW1dt2zZMu666y5GjRrF9OnTs/r22GMPCgoK+M1vfuNVMUmStNYMeZKaliXAW2SHudfI7Eu3GgtYwGu8VrEYyjSmscMROzDprkmrvVdu6dKlTJ48mVGjRjFz5sysvp/85CcUFBTwq1/9ynAnSZLWmffkKbW8J0/Mp8qG4rwFLK3B2A2ouDJX3LOYvU7bi+ll0ymjLOuw1W0dUFJSwm233caYMWP48MMPs/r23XdfCgoK+MUvfmG4k6R65j15SjOv5ElKh6+oOt1yBlU2FK/W5lS9f24TKjYQf/u5t3mn7J1qh65sE/DFixdz8803M3bsWD799NOsvgMOOID8/Hx+/vOf1/TsJEmSasyQpzoXQtgCyAd+CXQls5zFZGBUjHHJKsb9B9h3hebrY4yn1k2lahQi8CFVA93nNRibA2xLdpjrDaxme7eePXuSm5u70k3Ae/ToUfH8+++/58Ybb2TcuHHMnj0769iDDjqI/Px8fvKTn9SgWEmSpLVjyFN92JbMt9enkLm2siNwI9AWGLSasTcCBZWef18XBaqBWkZme4IVNxT/rgZjWwE7kR3odgLarHkZNdkEfMGCBVx33XVMmDCBr776KuuYQw89lPz8fH784x+v+ZtLkiStIUOe6lyM8WHg4UpNs0II2wCnsfqQ932M8Ys6K04Nx/dUv6H44hqM7UjmilzlQLcttfY33Ko2Ab/iiisYP348EydO5Ouvv84ad8QRR5Cfn8+uu+5aO4VIkiTVgCFPSekAzK3Bcf1DCH8AvgAeBIpijNVezQshtARaVmpqt85Vqm7MpfoNxctWMWa5jal6/9wWsJIdDmpFCIGWLVsyefJkrrjiCmbNmsX666/PnXfeyTbbbMO3336bdWzfvn3Jy8tjp512qruiJEmSVsKQp3oXQugFnMXqr+L9GfiIzN1WOwPjgG2AI1dy/DDgoloqU9WIMVJWVsbcuXOZOXMmPXv2pHPnzuTk5FS/OmQEPiV7quU0Mp9qTWxF1UC34TqfxlpZvgl4bm4u//jHP7j88suZN29eRX9OTg6///3vGTFiBNttt10yRUqSJOEWCloHIYSxwJDVHLZdjPHdSmM2AZ4E/hNjPHEN3++XwGNArxjjzGr6q7uS96lbKNSOGCMlJSUMGDCAqVOnVkxZ7NOnD5MmTaJl85aEGSET4l7hh1D39SpfNqM5sAPZYW4XGtS12K+//pqJEydy1VVXMX/+/Ir23Nxc/vCHPzB8+HC23nrrBCuUJK0Jt1BQmnklT+viEmDSao6ZtfwXIYSNgSeAZ4CT1+L9ni//2guoEvJijCVASaX3W4u30MqUlZUxYMAApkyZQgtasAu7sGvpruw6ZVc+euwjtl60NSyswQutRybAVQ50OwAt6rD4dfDll19y8cUXc+2117Jw4Q8n2KxZMwYMGMCwYcOyVteUJElKmiFPay3GOAeYU5Njy6/gPQG8DAyMMdbk7qsV9S7/OntVB6mWFQOvwqL/LuLgvxzMMIaxPdvTnOY/HLOyq3UbUnW6ZU8ya602cJ9//jkTJkzg+uuvZ9GiRRXtLVq04E9/+hNDhw5l8803T7BCSZKk6jldU3WuPOD9h8ydWMcDFZuNLV85s/yYx4DjYowvhBB6AscC/wC+IXNP3qXApzHGFffOW9n7tgfmOV1zDXxB1f3nqlwzrd7ijRfTaq9W2YGuG3W6IEpd+OSTTxg3bhw33XQTJSUVF4Zp2bIlJ598MhdeeCGbbrppghVKkmqD0zWVZl7JU304kMwUy15kluGobHkEaE5mUZXlu5gtAQ4AziWzn94nwL3AyDqutWmIZCbSrhjoarBZxTKW8Q7vMK3Sf2/kvMG7r75Lqy6t6rLqOvXhhx8yduxYbrnlFpYuXVrR3rp1a0499VQGDx5Mt27dEqxQkiSpZgx5qnMxxkms5t69GOOHVLrmE2P8BKjRFTutxlLgHapuKF6Tn1m2JnMNdVco26WMvHvzuPTfl7J4hc3r+h3dj86dO9dq2fVl5syZjB49mttvv51ly5ZVtLdt25YzzjiDCy64gA03TGhJT0mSpLVgyJPSZCHwOtmB7k0qLUezCp2oev/c1lT8LRFioGBAAR8M/KDKhuC33norOTmN4Ea7SqZPn87o0aO58847KS2tmEFMu3btOPvsszn33HPZYIMNEqxQkiRp7XhPnlIr9ffkfUPV6ZbvUbMNxTelaqDrzmrvn6u8T96sWbPo0aPHqvfJa4DeeustRo0axZQpUygr++F/VocOHTj33HM555xz6NSpU4IVSpLqg/fkKc28kic1dJHMHYkrBrpPajA2kLkaVznM9Qa6rF0pyzcE79KlC126rOWLJOT111+nqKiIe++9l8o/3OrcuTPnn38+Z5555vJ/7CVJkho1Q57UkJSSuRq3YqCbW4OxLYAdyQ50O5PZl64Je+WVVygqKuL+++/Pau/SpQsXXHABp59+Ou3aNaBd1yVJktaRIU9KymIy98tVDnOvA9/XYGw7MlfkKge67WiwG4on4fnnn6eoqIiHHnooq32jjTbiwgsv5JRTTqFt27YJVSdJklR3DHlSfZhHZkXLyoHuHWDZKsYstxFV75/rQaPYUDwJ//vf/ygqKuKRRx7Jat94440ZMmQIJ510Eq1bt06oOkmSpLpnyJNq22yqTrecVcOxPaga6NyarUaefPJJCgsLefzxx7PaN9tsM4YNG8bAgQNp1arx7uMnSZJUU4Y8aW2VUf2G4l/WYGwusD1VF0Rx3Y81EmPk8ccfp7CwkKeeeiqrb8stt2T48OEcd9xxtGjhPFZJktR0GPKkmlgKvE3VDcXn12BsGyo2FK947Ah4UWmtxRh55JFHKCws5Nlnn83q69WrFyNGjKB///40b948oQolSZKSY8iTVrSA6jcUX1KDsZ2pfkPx3DqptMmJMfL3v/+dwsJCXnrppay+bbfdlry8PI455hiaNfOvNkmS1HT5nZCatjlUXRDlPTJ7063OZlQNdJux2g3FtebKysp44IEHKCoqYtq0aVl9O+64I3l5efTp04fcXNO0JEmSIU9NQwQ+our9c5/VYGwAtqFqoFu/TipVJaWlpdx7770UFRXx5ptvZvXtsssuFBQUcPjhh5OT41KjkiRJyxnylGoTmECb37bJTLf8tgYDWgA7UXVDcbdTq1fLli1jypQpjBo1infeeSerb/fdd6egoIBDDz2UELxsKkmStKIQY03mpUmNTwihfSTOW+kB7cle2XL5huKu1ZGYZcuWceeddzJq1Cjef//9rL699tqLgoICDjroIMOdJGmdFRcX06FDB4AOMcbipOuRapNX8tQ0dKPqdMst8f65BmLJkiXcfvvtjBkzhlmzsjcV/OlPf8pFF13E/vvvb7iTJEmqAUOeUu0gDuKe9++hXa92SZeiapSUlHDrrbcyZswYPv7446y+X/ziFxQUFLDvvvsa7iRJktaAIU+p9giPEDd0SnJDs2jRIm666SbGjRvHZ59lr37zq1/9ivz8fH76058mVJ0kSVLjZsiTVG++//57rr/+esaPH88XX3yR1XfIIYeQn5/PnnvumVB1kiRJ6WDIk1TnFixYwDXXXMMll1zCV199ldX3u9/9jvz8fHbfffeEqpMkSUoXQ56kOlNcXMxVV13FxIkT+eabb7L6jjrqKPLy8ujdu3cyxUmSJKWUIU9Srfv222+54ooruOyyy/juu+8q2kMIHHPMMYwYMYIdd9wxuQIlSZJSzJAnqdZ88803XHrppVx55ZUUF/+w5VBOTg79+/dn+PDhbLvttglWKEmSlH6GPEnr7KuvvmLixIlcffXVLFiwoKI9NzeX4447juHDh9OrV68EK5QkSWo6DHmS1toXX3zBhAkTuO666/j+++8r2ps3b87AgQMZOnQoW265ZYIVSpIkNT2GPElr7LPPPmP8+PHccMMNLF68uKK9RYsWnHTSSVx44YV07949wQolSZKaLkOepBr7+OOPGTt2LDfffDNLliypaG/VqhWnnHIKgwcPZpNNNkmwQkmSJBnyJK3WBx98wJgxY5g0aRJLly6taG/Tpg2nnXYagwYNomvXrglWKEmSpOUMeZJW6v3332f06NHccccdlJaWVrSvt956nHnmmZx//vl06dIlwQolSZK0IkOepCreeecdRo0axV133UVZWVlFe/v27TnnnHM455xzWH/99ROsUJIkSStjyJNU4c0332TkyJH85S9/IcZY0d6xY0fOO+88zj77bDp27JhcgZIkSVotQ54kXn31VYqKirjvvvuy2tdff30uuOACzjjjDNq3b59QdZIkSVoThjypCXvppZcoKirib3/7W1b7hhtuyKBBgzjttNNYb731EqpOkiRJa8OQJzVBzz77LEVFRfzzn//Mau/atStDhgzh5JNPpk2bNglVJ0mSpHVhyJOakP/+978UFRXxr3/9K6t90003ZciQIZxwwgm0bt06oeokSZJUGwx5UsrFGPnPf/5DYWEh//nPf7L6Nt98c4YNG8aAAQNo2bJlMgVKkiSpVhnypJSKMfKvf/2LoqIinn766ay+Hj16MGLECP74xz/SvHnzhCqUJElSXTDkSSkTY+Sf//wnhYWFPP/881l9W221FXl5eRx77LE0a+Yff0mSpDTyuzwpJWKM/O1vf6OoqIiXX345q2+77bYjPz+fo48+mtzc3IQqlCRJUn0w5EmNXFlZGffddx8jR47ktddey+rbaaedyM/P56ijjiInJyehCiVJklSfDHlSI1VaWso999zDyJEjeeutt7L6dt11VwoKCjjssMMMd5IkSU2MIU9qZJYtW8bdd9/NyJEjmT59elbfHnvsQX5+PocccgghhIQqlCRJUpIMeVIjsXTpUiZPnsyoUaOYOXNmVt9PfvITCgoK+NWvfmW4kyRJauIMeVIDt2TJEiZNmsSYMWP48MMPs/r23XdfCgoK+MUvfmG4kyRJEmDIkxqsxYsXc8sttzB27Fg++eSTrL7999+f/Px89t1334SqkyRJUkPligyqFyGED0MIcYXH0NWMaRVCuDqE8E0IYUEI4d4Qwkb1VXNSFi1axOWXX07Pnj0544wzsgLeQQcdxP/+9z/+/e9/G/AkSZJULa/kqT4VADdWej5/NcdfChwC9AXmAVcB9wH71El1CVu4cCHXXXcdEyZM4Msvv8zqO/TQQ8nLy2OPPfZIqDpJkiQ1FoY81af5McYvanJgCKEDcAJwbIzx8fK2gcA7IYS9YozP1WGd9Wr+/PlcffXVXHLJJXz99ddZfUcccQR5eXnstttuCVUnSZKkxsbpmqpPQ8unXk4LIQwOIazqhwy7A82Bfy9viDG+C3wM7F3HddaLefPmMXLkSLbYYguGDRtWEfBCCBx99NG89tpr3HfffQY8SZIkrRGv5Km+XAG8AswFfgKMAboB56/k+K7Akhjjdyu0f1neV0UIoSXQslJTu3Wot87MnTuXyy+/nMsvv5x58+ZVtOfk5NCvXz9GjBjB9ttvn2CFkiRJaswMeVprIYSxwJDVHLZdjPHdGOPESm2vhxCWANeHEIbFGEtqqaRhwEW19Fq17uuvv2bixIlcddVVzJ//w+2Iubm5/OEPf2D48OFsvfXWCVYoSZKkNDDkaV1cAkxazTGzVtL+PJnff1sA06vp/wJoEULouMLVvI3K+6ozBqgcJtsBn66mvjr35Zdfcskll3DNNdewcOHCivZmzZpx/PHHM2zYMHr27JlghZIkSUoTQ57WWoxxDjBnLYf3BsqAr1bS/zKwFNgfuBcghLAN0B14diX1lAAVVwWT3hz8888/Z8KECVx//fUsWrSoor158+accMIJDB06lM033zzBCiVJkpRGhjzVuRDC3sCewBNktk3Ym8z2CJNjjN+WH7MJ8BhwXIzxhRjjvBDCzcDEEMJcoBi4Eni2oa+s+cknnzB+/HhuvPFGSkp+mInasmVLTjrpJC688EI222yzBCuUJElSmhnyVB9KgH7A/5FZGOUDMiGv8tTK5sA2QJtKbeeRudp3b/m4R4DT677ctfPhhx8yduxYbrnlFpYuXVrR3rp1a0499VQGDx5Mt27dEqxQkiRJTUGIMSZdg1QnQgjtgXnz5s2jffv2dfY+M2fOZMyYMdx2220sW7asor1t27acfvrpXHDBBWy00UZ19v6SJGnNFRcX06FDB4AOMcbipOuRapNX8qS1NH36dEaPHs2dd95JaWlpRXu7du0466yzOO+889hggw0SrFCSJElNkSFPWkNvv/02I0eOZMqUKZSVlVW0d+jQgXPPPZezzz6bzp07J1ihJEmSmjJDnlRDr7/+OiNHjmTq1KlUnubcuXNnzjvvPM4666zl0z4kSZKkxBjypNV45ZVXKCoq4v77789q32CDDRg0aBCnn3467dq1S6Y4SZIkaQWGPGklXnjhBYqKivj73/+e1b7RRhsxePBgTj31VNq2bZtQdZIkSVL1DHnSCp555hkKCwt55JFHsto33nhjhgwZwkknnUTr1q0Tqk6SJElaNUOeVO7JJ5+kqKiIxx57LKt9s802Y+jQofzpT3+iVatWCVUnSZIk1YwhT01ajJHHH3+cwsJCnnrqqay+LbbYguHDh3P88cfTokWLhCqUJEmS1owhT01SjJFHHnmEwsJCnn322ay+Xr16MWLECPr370/z5s0TqlCSJElaO4Y8NSkxRh566CEKCwt58cUXs/q23XZbRowYQb9+/WjWzD8akiRJapz8TlZNQllZGQ888ABFRUVMmzYtq2+HHXYgPz+fPn36kJubm1CFkiRJUu0w5Cn17rvvPiZOnMgbb7yR1b7LLruQn5/PEUccQU5OTkLVSZIkSbUrxBiTrkGqEyGE9sC8Fdt79+7NkCFDOPjggwkhJFCZJElKWnFxMZttthlAhxhjcdL1SLXJkKfUCiFsAnyadB2SJKlB2zTG+FnSRUi1yZCn1AqZy3QbA/OTrqWG2pEJpZvSeGquLU313JvqeUPTPfemet7QdM+9qZ43NI5zbwd8Hv2GWCnjPXlKrfK/sBvNT+YqTR2d39SmjTTVc2+q5w1N99yb6nlD0z33pnre0GjOvaHWJa0TV5uQJEmSpBQx5EmSJElSihjypIajBPh/5V+bmqZ67k31vKHpnntTPW9ouufeVM8bmva5S4ly4RVJkiRJShGv5EmSJElSihjyJEmSJClFDHmSJEmSlCKGPCkhIYQtQgg3hxA+CCEsCiHMDCH8vxBCi9WMaxVCuDqE8E0IYUEI4d4Qwkb1VXdtCCGMCCE8E0L4PoTwXQ3HTAohxBUeD9dxqbVuLc89hBAKQwizy3+v/DuEsFUdl1rrQgidQwh3hhCKQwjflf/+X281Y/5Tzed+XX3VvDZCCGeEED4MISwOITwfQthjNcf3DSG8W378GyGE39RXrbVtTc49hDCgms92cX3WWxtCCD8PITwYQvi8/BwOr8GY/UIIr4QQSkIIM0IIA+q+0tq1puddfs4rft4xhNC1nkqWmhRDnpScbcn8GTwF2AE4DzgVGL2acZcChwJ9gX2BjYH76q7MOtECuAe4dg3HPQx0q/T4fS3XVR/W5twvBM4m8/tjT2Ah8EgIoVXtl1en7iTze/1A4LfAz4EbajDuRrI/9wvrqsB1FUI4BphIZkXB3YDXyHxWG67k+J8AdwE3A7sC9wP3hxB2rJeCa9Gannu5YrI/283rus460JbMuZ5Rk4NDCFsCDwFPAL2By4CbQgi/rqP66soanXcl25D9mX9Vy3VJwtU1pQYlhDAYOC3G2GMl/R2AOcCxMcap5W3bAu8Ae8cYn6u3YmtB+U+vL4sxdqzBsZOAjjHGw+u2qvpR03MPIQTgc+CSGOPF5W0dgC+BATHGu+u41FoRQtgOeBv4cYzxpfK2g4B/AJvGGD9fybj/AK/GGM+tp1LXSQjheeDFGOOZ5c9zgE+AK2OMY6s5fgrQNsb420ptz5E551PrqexasRbnPoAa/vlvLEIIETgixnj/Ko4ZBxwSY9yxUtvdZP5+O6juq6x9NTzv/cgE204xxu/qpTCpCfNKntSwdADmrqJ/d6A58O/lDTHGd4GPgb3rtrQGYb8QwlchhOkhhGtDCOsnXVA92BLoSvZnPg94nsb1me8NfLc84JX7N1BG5urkqvQPIXwdQngzhDAmhNCmzqpcB+VTrXcn+7MqK3++ss9q78rHl3tkFcc3SGt57gDrhRA+CiF8EkJ4IISwQx2X2hCk4jNfB6+WTz3/Vwhhn6SLkdLKkCc1ECGEXsBZwPWrOKwrsKSan4J+Wd6XZg8DxwH7A0PITFX9ZwghN9Gq6t7yz/XLFdob22felRWmZcUYl5H5ocaqzuPPwB+AXwBjgD8Ck+uoxnW1AZDLmn1WXdfw+IZqbc59OvAn4HdkPuMc4JkQwqZ1VWQDsbLPvH0IoXUC9dSX2WSmnB9V/vgE+E8IYbdEq5JSqlnSBUhpE0IYSyaErMp25Vfglo/ZhEyIuSfGeGNd1ldX1ua818QK0xLfCCG8DswE9gMeW5vXrC11fe4NWU3PfW1fP8ZY+Z69N0IIs4HHQgg9Y4wz1/Z1lbwY47PAs8ufhxCeITP1/BQgP6m6VDdijNPJBPvlngkh9CRzP/ofk6lKSi9DnlT7LgEmreaYWct/EULYmMx9Cs8AJ69m3BdAixBCxxWu5m1U3pekNTrvdRVjnBVC+BroRcIhj7o99+Wf60ZkfhJOpeevruVr1qaanvsXQNYCHCGEZkBn1uz37vPlX3uRCfkNyddAKZnPprJV/fn8Yg2Pb6jW5tyzxBiXhhCmkfls02xln3lxjHFRAvUk6QXgp0kXIaWRIU+qZTHGOWQWR1mt8it4TwAvAwPL72FZlZeBpWSmLN5b/hrbAN2p9BPxJKzJedeG8ild65MdfBJRx+f+AZlvCvenPNSFENqTuY9tTVcnrXU1PfcQwrNAxxDC7jHGl8ubf0lmit7zKx9ZRe/yr4l/7iuKMS4JIbxM5rO6HyoWH9kfuGolw54t77+sUtuBJPzneU2t5blnKZ96vROZxXjS7FlgxW0yGt1nXkt60wD/LEtp4D15UkLKA95/yCyaMgjoEkLoWnnPoBDCJuX7Z+0BFQtu3AxMDCH8IoSwO3Ar8GxjWlkzhNA9hNCbTDjNDSH0Ln+sV+mYd0MIR5T/er0QwoQQwl4hs7/g/sADwAwyCxY0Gmt67jGzBPJlQF4I4bAQwk7A7WRW3Ly/vutfWzHGd8hMSb4xhLBH+YILVwF3L19Zc8Xf7yGEniGE/BDC7uWf+2Fkzv2pGOPrSZ3LakwETgohHF++oui1ZJaavxUghHB7CGFMpeMvBw4KIVwQQtg2hPB/wI+oYTBqYNbo3EMIBSGEX4UQepTflzWZzBYKNyVQ+1or//upd/mfa4Aty593L+8fE0K4vdKQ64AeIYTx5Z/56cDRZLbHaTTW9LxDCOeGEH4XQugVQtgxhHAZmR/0XF3vxUtNgFfypOQcSGZaUi/g0xX6QvnX5mT2FKq8muB5ZFYkvBdoSSbknF6nlda+QuD4Ss+nlX/9BZngC5nz7lD+61Jg5/IxHckEnEeB/BhjSR3XWtvW9NwBxpP5ZvkGMuf/NHBQjLGxbRzdn0x4eYwffg+fXal/xd/vS4ADgHPJnP8n5WNG1k+5ay7GOCWE0IXM59yVzNXXg2KMyxfa6E7m3Jcf/0wI4Vgy5zQaeB84PMb4Zr0WXgvW9NyBTmT2QOwKfEtmpsJPYoxv11vRteNHZGZkLDex/OttwAAye8F1X94ZY/wghHAImVB3Dpm//0+MMTaqH1ixhudNZo/QS4BNgO+B14EDYoyVX0NSLXGfPEmSJElKEadrSpIkSVKKGPIkSZIkKUUMeZIkSZKUIoY8SZIkSUoRQ54kSZIkpYghT5IkSZJSxJAnSZIkSSliyJMkSZKkFDHkSZIkSVKKGPIkSZIkKUUMeZIkSZKUIoY8SZIkSUoRQ54kKbVCCJuEEBaHEG5Zof2AEMLSEMKlSdUmSVJdCTHGpGuQJKnOhBCuAk4GtooxfhRC2BZ4FvgvcHiMsSzRAiVJqmWGPElSqoUQNgFmArcA+cDzwHzgpzHGhUnWJklSXWiWdAGSJNWlGONnIYQbgZOA3YDWwL4GPElSWnklT5KUeiGEzYEPgUXAz2KMLydbkSRJdceFVyRJTcGI8q/NgLlJFiJJUl0z5EmSUi2EMBg4ETgTWMYPgU+SpFQy5EmSUiuEcDgwFsiPMV4N3AAcF0LYMtHCJEmqQ96TJ0lKpRDC7sBTwL0xxuPK2zYGZgGTY4wnJlmfJEl1xZAnSUqdEMKmwAtkAt3+McaSSn3XkJm+uU2M8YOESpQkqc4Y8iRJkiQpRbwnT5IkSZJSxJAnSZIkSSliyJMkSZKkFDHkSZIkSVKKGPIkSZIkKUUMeZIkSZKUIoY8SZIkSUoRQ54kSZIkpYghT5IkSZJSxJAnSZIkSSliyJMkSZKkFDHkSZIkSVKKGPIkSZIkKUX+P88oP5FLrh75AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 900x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# find best set of weights from gradient descent run on Least Absolute Deviations cost \n",
    "ind = np.argmin(cost_history_2)\n",
    "absolute_weights = weight_history_2[ind]\n",
    "demo.plot_fit(plotting_weights = [least_weights,absolute_weights])"
   ]
  }
 ],
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   "include_colab_link": true,
   "provenance": []
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.15"
  },
  "toc": {
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 "nbformat": 4,
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